Lattice Boltzmann (LB) techniques are used to simulate a first order reaction occurring in a variety of porous catalyst pellet shapes; namely spheres, cylinders and trilobes. This enables a relationship between the effectiveness factor and the Thiele modulus for individual pellets to be determined. In the case of single pellets for an infinite flow rate, good agreement is produced between the simulations and analytical/semi-analytical descriptions of this relationship. The effect of flow rate on this relationship is then explored and quantified. Finally the simulations are applied to 3D random packings of the various pellet shapes. Reasonably good agreement with respect to the mean effectiveness factor is produced when the analytical/semi-analytical description is applied to the respective pellet size distributions. By comparison with the simulations however, the analytical/semi-analytical descriptions tended to under-predict the standard deviation of the effectiveness factor distributions, suggesting an additional influence due to local random packing and hence flow heterogeneity. (C) 2011 Published by Elsevier Ltd.